利用残差控制的快速圆弧生成与反走样算法

Fast Algorithms for Generating and Anti-aliased Drawing Circles Controlled by Residuals

圆弧的生成和反走样绘制是图形学领域的重要问题.为了提高圆弧的生成速度,提出一种直接利用残差递推实现的基本圆弧生成算法.该算法直接以变形后的残差作为判别依据,消除了迭代中的常数项加法,且每次步进可以方便地转换为灰度,进而构成一种整数反走样绘制算法,这2种算法具有十分相近的结构,且比同类算法效率更高;然后,引入2步迭代参数控制,并视圆弧为水平线段和斜线段逼近而成,推广得到了一种双步行程算法.理论分析和实验表明,文中算法比传统算法的绘制效率提高0.7倍以上.

How to generate and anti-aliased draw circles is an important problem of computer graphics. In order to improve the circle drawing speed, a basic circle generating algorithm is presented. In the algorithm, residuals rather than intermediate data are used as decision parameters, the addition of constant in every loop is eliminated. Since grey conversion can be obtained in a simple manner, the algorithm may he easily developed into an integral anti aliased algorithm. Two algorithms are constructed by quite similar structure, and are all more effective than other algorithms. By calculating and drawing slices one by one with double-step technique, the developed run-length algorithm can effectively increase the circle drawing speed due to the great reduction of operations. The experiment results prove that the circle-drawing speed of the run length algorithm can be almost 1.7 times comparing with that of basic algorithm.